Trends in Computational Nanomechanics (eBook)

Dr. Traian Dumitrica received a doctorate in physics from Texas A&M University in 2000. Since then he has worked at Rice University, Freie Universitaet Berlin, and Universitaet Kassel. He joined the University of Minnesota faculty in 2005. His research focuses in understanding the mechanical properties of materials using atomistic computational methods. System of interest include carbon nanotubes, silicon nanoparticles, and coherent phonons in semiconductors.

Preface 6
Contents 10
1 Hybrid Quantum/Classical Modeling of Material Systems: The ``Learn on the Fly'' Molecular Dynamics Scheme 20
1.1 Introduction 20
1.2 The LOTF Scheme 21
1.3.1 Reconciling the Boundary 21
1.3.2 Evaluation of the QM Forces 23
1.3.3 Force Matching 24
1.3.3.1 The Adjustable Potential 25
1.3.4 The LOTF Predictor-Corrector Scheme 26
1.3 Selection of the QM Region: An Hysteretic Algorithm 29
1.4.1 A Screw Dislocation Study 30
1.4.2 Brittle Fracture 31
1.4 Towards Chemical Complexity: Hydrogen-Induced Platelets in Silicon 34
1.5.1 The Atom-Resolved Stress Tensor 37
1.5 Acknowledgments 40
References 40
2 Multiscale Molecular Dynamics and the Reverse Mapping Problem 43
2.1 Introduction 43
2.2.1 Atomistic and Coarse-Grained Molecular Dynamics 46
2.2.2 Mapping Between Different Representations, or the Reverse Mapping Problem 47
2.2 Adaptive Multiscale Molecular Dynamics 48
2.3.1 Stage 1: Coupling Atomistic and Coarse-Grained Regions 49
2.3.2 Equations of Motion 55
2.3.3 Stage 2: Freezing the Intra-Bead Motions 56
2.3.4 Case Study 1: Liquid Methane 58
2.3.5 Other Adaptive Multiscale Implementations 60
2.3 Reverse Mapping Through Rigid Body Rotation 61
2.4.1 Rigid Body Rotational Optimization 62
2.4.2 Rigid Body Rotational Dynamics 65
2.4.3 Coupling Between the Rotational Dynamics and Coarse-Grained Molecular Dynamics 66
2.4.4 Case Study 2: Polyethylene Chain 68
2.4 Combining Rotational Reverse Mapping with Hybrid MD 71
2.5.1 Case Study 3: Hybrid Simulation of a Polyethylene Chain 72
2.5 Summary 75
2.6 Acknowledgments 75
References 76
3 Transition Path Sampling Studies of Solid-Solid Transformations in Nanocrystals under Pressure 78
3.1 Rare Events in Computer Simulations 78
3.2 Transition Path Sampling 81
3.3.1 The Transition Path Ensemble 81
3.3.2 Monte Carlo in Trajectory Space 83
3.3.3 Analyzing Trajectories 86
3.3.4 Calculating Rate Constants 88
3.3 A TPS Algorithm for Nanocrystals in a Pressure Bath 91
3.4.1 Ideal Gas Pressure Bath 91
3.4.1.1 Algorithm 92
3.4.2 Simple Shooting Moves 94
3.4 The Wurtzite to Rocksalt Transformation in CdSe Nanocrystals 95
3.5.1 Straightforward MD Simulations 96
3.5.2 TPS Reveals the Main Mechanism 98
3.5 Concluding Remarks 98
3.6 Acknowledgments 99
References 99
4 Nonequilibrium Molecular Dynamics and Multiscale Modeling of Heat Conduction in Solids 102
4.1 Introduction 102
4.2 Molecular Dynamics and its Applicability to the Simulation of Heat Transport 104
4.3.1 Introduction to Equilibrium MD 104
4.3.2 Temperature Control 106
4.3.3 Lattice Vibrations 107
4.3.4 The Quantum Model of Phonon Heat Transport 108
4.3.5 The Classical Limit 112
4.3.6 Heat Transport in Metals 115
4.3 Nonequilibrium Molecular Dynamics 116
4.4.1 The Green-Kubo Method 117
4.4.2 The Direct Method 117
4.4.3 Size Effects 123
4.4 Isothermal Concurrent Multiscale Methods 126
4.5.1 Coarse-Grained Dynamics 128
4.5.2 Coarse-Grained Thermal Properties 132
4.5.3 Boundary Conditions for the Atomistic/Continuum Interface 134
4.5.4 Isothermal Dynamic Multiscale Models 138
4.5 Non-Isothermal Concurrent Multiscale Methods 139
4.6.1 Quasi-Static Phonon Models for Insulators 140
4.6.2 Dynamic Phonon Models for Insulators 143
4.6.3 Quasi-Static Models for Metals 144
4.6.4 Dynamic Coarse-Grained Models for Metals 145
4.6.5 Conclusions 146
4.6 ACKNOWLEDGEMENT 147
REFERENCES 147
5 A Multiscale Methodology to Approach Nanoscale Thermal Transport 152
5.1 Introduction 152
5.2.1 Interfacial Resistance 153
5.2.2 Phonon Behavior Through Acoustic Waves 153
5.2.3 Strategies to Modulate the Interfacial Resistance 154
5.2.4 Role of Surface Modifications 154
5.2 Continuum Limits 155
5.3 Multiscale Investigations 156
5.4.1 Atomistic and Multiscale Simulations 156
5.4.2 Molecular Dynamics (MD) Simulations 158
5.4.3 Thermal Lattice Boltzmann Method (LBM) 159
5.4.4 Hybrid Multiscale Methodology 160
5.4.5 Coupling MD and LBM 161
5.4 Example Problems 163
5.5 Acknowledgments 163
REFERENCES 163
6 Multiscale Modeling of Contact-Induced Plasticity in Nanocrystalline Metals 168
6.1 Introduction 168
6.2 Atomistic Modeling of Nanoscale Contact in Nanocrystalline Films 171
6.3.1 Simulation Methods 172
6.3.1.1 Molecular Dynamics 172
6.3.1.2 Quasicontinuum (QC) Method 172
6.3.2 Modeling of Spherical/Cylindrical Contact in Nanocrystalline Metals 173
6.3.3 Calculations of Local Stresses and Mean Contact Pressures 175
6.3.4 Tools for the Visualization of Defects and Grain Boundaries 177
6.3.4.1 Centro-Symmetry Parameter 177
6.3.4.2 Local Crystal Structure by Ackland and Jones 178
6.3 Effects of Interatomic Potentials on Equilibrium Microstructures 178
6.4 Effects of a Grain Boundary Network on Incipient Plasticity During Nanoscale Contact 180
6.5 Mechanisms of Grain Boundary Motion During Contact Plasticity 183
6.6 Concluding Remarks 187
6.7 Acknowledgment 187
References 188
7 Silicon Nanowires: From Empirical to First Principles Modeling 190
7.1 Introduction 190
7.2 Methodological Considerations 193
7.3.1 Empirical Models 194
7.3.2 Semi-Empirical Models 195
7.3 Structural Properties: Application of Empirical Methods 197
7.4 Morphology of Thin Silicon Nanowires: Application of Tight Binding and First Principles Methods 200
7.5 Conclusions 205
References 206
8 Multiscale Modeling of Surface Effects on the Mechanical Behavior and Properties of Nanowires 209
8.1 Introduction 209
8.2 Methodology 212
8.3.1 Continuum Mechanics Preliminaries 212
8.3.2 Surface and Bulk Energy Densities 213
8.3.3 Formulation for Embedded Atom Method/FCC Metals 215
8.3.4 Formulation for Diamond Cubic Lattices 219
8.3.4.1 Bulk Cauchy-Born Model for Silicon 219
8.3.4.2 Surface Cauchy-Born Model for Silicon 222
8.3 Finite Element Formulation and Implementation 224
8.4.1 Variational Formulation 224
8.4.2 Finite Element Eigenvalue Problem for Nanowire Resonant Frequencies 225
8.4 Applications of Surface Cauchy-Born Model 226
8.5 Direct Surface Cauchy-Born/Molecular Statics Comparison 226
8.6 Surface Stress Effects on the Resonant Properties of Silicon Nanowires 228
8.7.1 Constant Cross Sectional Area 231
8.7.2 Constant Length 233
8.7.3 Constant Surface Area to Volume Ratio 234
8.7 Discussion and Analysis 235
8.8.1 Comparison to Experiment 237
8.8 Conclusions and Perspectives 239
8.9 Acknowledgments 240
References 240
9 Predicting the Atomic Configuration of 1- and 2-Dimensional Nanostructures via Global Optimization Methods 246
9.1 Introduction 246
9.2 Reconstruction of Silicon Surfaces as a Problem of Global Optimization 249
9.3.1 The Parallel-Tempering Monte Carlo 250
9.3.2 Genetic Algorithm 254
9.3.3 Selected Results on Si(114) 256
9.3 The Structure of Freestanding Nanowires 258
9.4.1 A Genetic Algorithm for 1-D Nanowire Systems 258
9.4.2 Magic Structures of H-Passivated Si-[110] Nanowires 261
9.4.3 Growth of 1-D Nanostructures into Global Minima Under Radial Confinement 262
9.4 Future Directions 265
9.5 Acknowledgments 266
References 266
10 Atomic-Scale Simulations of the Mechanical Behavior of Carbon Nanotube Systems 269
10.1 Introduction 269
10.2 Computational Details 270
10.3.1 Interatomic Potentials 271
10.3.2 Important Approximations 274
10.3.2.1 Periodic Boundary Conditions 274
10.3.2.2 Temperature Control 275
10.3.2.3 Predictor-Corrector Algorithm 276
10.3.2.4 Simulation Methods for Mechanical Behavior 277
10.3 Mechanical Behavior of Nanotubes 278
10.4.1 Tensile Behavior 279
10.4.1.1 Young's Modulus 279
10.4.1.2 Fracture or Plastic Behavior 280
10.4.1.3 Effect of Filling, Functionalization, and Temperature 281
10.4.1.4 Effect of Combined Loads 282
10.4.2 Compressive Behavior 285
10.4.2.1 Buckling Instability 285
10.4.2.2 Effect of Filling, Functionalization, and Temperature 287
10.4.2.3 Nanotube Proximal Probe Tips 289
10.4.2.4 Crystalline Bundle 290
10.4.3 Bending Behavior 290
10.4.3.1 Bending Modulus 290
10.4.3.2 Buckling Instability 291
10.4.3.3 Effect of Filling, Functionalization, and Temperature 291
10.4.3.4 Effect of External Gases 292
10.4.4 Torsional Behavior 294
10.4.4.1 Shear Modulus and Stiffness 294
10.4.4.2 Buckling Instability 296
10.4.4.3 Effect of Filling, Functionalization, and Temperature 297
10.4.4.4 Effect of Combined Loads 300
10.4.4.5 Crystalline Bundle 305
10.4 Conclusions 305
10.5 Acknowledgments 306
REFERENCES 306
11 Stick-Spiral Model for Studying Mechanical Properties of Carbon Nanotubes 310
11.1 Introduction 310
11.2 Carbon Nanotubes and Their Mechanical Properties 311
11.3.1 Carbon Nanotubes (CNTs) 311
11.3.2 Mechanical Properties of CNTs 313
11.3.3 Theoretical Modeling on Geometry Dependent Mechanical Properties of CNTs 313
11.3 Stick-Spiral Model For Carbon Nanotubes 315
11.4.1 Model Description 315
11.4.2 Governing Equations of the Stick-Spiral Model 317
11.4.3 Linear Stick-Spiral Model and its Applications 319
11.4.3.1 Linear Stick-Spiral Model 319
11.4.3.2 Elastic Mechanical Properties of SWCNTs 319
11.4.3.3 Explicit Expressions for Vibrating Frequencies of Some Raman Modes 321
11.4.4 Nonlinear Stick-Spiral Model and its Applications 323
11.4.4.1 Nonlinear Stick-Spiral Model 323
11.4.4.2 Mechanical Behavior of SWCNTs Under Large Strains 324
11.4 Concluding Remarks 327
11.5 Acknowledgments 328
11.5 Appendix 328
References 330
12 Potentials for van der Waals Interaction in Nano-Scale Computation 336
12.1 Introduction 336
12.2 Potentials for van der Waals Interaction 337
12.3.1 The Lennard-Jones Potential 337
12.3.2 The Registry-Dependent Interlayer Potential 337
12.3 Computational Method 337
12.4 Comparison Between the Two Potentials 340
12.5.1 On the Lattice Registry Effect 340
12.5.2 On the Deformation of Carbon Nanotubes 342
12.5 Concluding Remarks 345
REFERENCES 345
13 Electrical Conduction in Carbon Nanotubes under Mechanical Deformations 347
13.1 Introduction 347
13.2 Modeling Procedures 351
13.3.1 The Carbon Nanotube Wall 352
13.3.2 Initial Internal Stress State 354
13.3.3 Construction of Special Interaction Elements 355
13.3.4 Model of the Inter-Layer Shear Resistance 356
13.3.5 Electrical Transport Model 356
13.3 Numerical Results 357
13.4.1 Bending of SWNTs 357
13.4.2 Tube-Tube-Substrate Interaction 358
13.4.3 Deformation of MWNTs Under Bending 359
13.4.4 Laterally-Squeezed (8, 8) SWNT 363
13.4.5 Bent (10, 0) SWNT 365
13.4.6 Simulation of Laboratory Experiments on a MWNT 366
13.4.7 Effect of the Outer Diameter on the Conductance of MWNTs Under Bending 368
13.4.8 Effect of the Outer Diameter on the Conductance of MWNTs Under Stretching 372
13.4.9 Effect of Current Saturation -- Non-Linear I-V Response 373
13.4 Conclusions 374
References 375
14 Multiscale Modeling of Carbon Nanotubes 378
14.1 Introduction 378
14.2 Multiscale Coupling Approaches 379
14.3.1 Quasi-Continuum Method 380
14.3.2 Bridging Domain Method 381
14.3.3 Bridging Scale Method 382
14.3 Brenner Potential 383
14.4 An Atomic Simulation Method 385
14.5 A Higher-Order Continuum Model 387
14.6.1 Higher-Order Gradient Continuum 388
14.6.2 Constitutive Relationship 390
14.6.3 Mesh-Free Numerical Simulation 391
14.6 Multiscale Coupling Scheme 392
14.7 Multiscale Computational Examples 393
14.8.1 Bending Test 394
14.8.2 Tensile Failure of SWCNTs with a Single-Atom Vacancy Defect 395
14.8 Summary 397
References 398
15 Quasicontinuum Simulations of Deformations of CarbonNanotubes 400
15.1 Introduction 400
15.2 Quasicontinuum Method for Carbon Nanotubes 402
15.3.1 Deformations of Single-Walled CNTs 403
15.3.2 Bravais Multilattice and Inner Displacement 405
15.3.3 Interpolation Function 407
15.3.4 Summation and Minimization of Energy 409
15.3.5 Adaptive Meshing Scheme 413
15.3.6 Deformation of Multiwalled Carbon Nanotubes (MWCNTs) 413
15.3.7 Numerical Examples 414
15.3.7.1 Bonding and Nonbonding Interaction for CNT 414
15.3.7.2 Bending Simulations for a SWCNT 415
15.3 QC Method for CNTS by Use of Variable-Node Elements 417
15.4.1 Variable Node Elements for QC 418
15.4.2 Numerical Examples 422
15.4 Conclusions 424
15.5 Acknowledgment 425
15.5 Appendix A. The Green Strain in Deformation of a CNT 425
15.5 Appendix B. The Functions and the Parameters in the Tersoff-Brenner Potential 426
15.5 Appendix C. The Shape Functions for a 24-noded Variable-Node Element 427
References 430
16 Electronic Properties and Reactivities of Perfect, Defected, and Doped Single-Walled Carbon Nanotubes 431
16.1 Scope 431
16.2 Introduction 431
16.3 Theoretical Methods 433
16.4.1 First-Principles Calculations 433
16.4.2 Semiempirical Quantum Mechanical Methods 434
16.4.3 Density-Functional Theory 436
16.4.4 ONIOM Model 436
16.4.5 Molecular Dynamical Simulations 437
16.4 Single-Walled Carbon Nanotubes 438
16.5.1 Perfect SWCNT Rods 438
16.5.2 Open-End SWCNT Segment 441
16.5 Vacancy-Defected Fullerenes and Swcnts 441
16.6.1 Vacancy-Defected Fullerenes 442
16.6.2 Vacancy-Defected SWCNTs 449
16.6.2.1 Vacancy-Defected (5,5) and (10,0) SWCNTs 449
16.6.2.2 Vacancy-Defected (5,5) SWCNT Clip 454
16.6 Doped SWCNTs 455
16.7.1 B- and N-Doped SWCNTs 455
16.7.2 Ni-, Pd-, and Sn-Doped SWCNTs 455
16.7.3 Chalcogen Se- and Te-Doped SWCNTs 458
16.7.4 Pt-Doped SWCNTs 458
16.7.5 Gas Adsorptions on Pt-Doped SWCNTs 461
16.7 Chemical Reactions of Vacancy-Defected SWCNT 463
16.8.1 Computational Details and Model Selection 463
16.8.2 Chemical Reaction of NO with Vacancy-Defected SWCNT 464
16.8.3 Chemical Reaction of O 3 with Vacancy-Defected SWCNT 467
16.8.3.1 Reaction of O 3 with the Active Carbon Atom 468
16.8.3.2 Reaction of O 3 with the C8-C9 Bond (Position 1) 468
16.8.3.3 Reaction of O 3 with the C6-C7 Bond (Position 2) 470
16.8.3.4 Reaction of O 3 with the C4-C5 Bond (Position 3) 471
16.8.3.5 Reaction of O 3 with the C2-C3 Bond (Position 4) 472
16.8.3.6 Ab initio Molecular Dynamics Studies 472
16.8 Conclusions and Outlooks 474
16.9 ACKNOWLEDGMENTS 475
References 475
17 Multiscale Modeling of Biological Protein Materials -- Deformation and Failure 482
17.1 Introduction 482
17.2.1 Nanomechanics of Protein Materials: Challenges and Opportunities 484
17.2.2 Strategy of Investigation 485
17.2.3 Impact of Materiomics 486
17.2.4 Transfer from Biological Protein Materials to Synthetic Materials 488
17.2 Atomistic Simulation Methods 488
17.3.1 Molecular Dynamics Formulation 488
17.3.2 CHARMM Force Field 491
17.3.3 ReaxFF Force Field 493
17.3.4 Coarse-Graining Approaches of Protein Structures 495
17.3.4.1 Single-Bead Models 496
17.3.4.2 Multi-Bead Models 498
17.3.4.3 Coarser Models 498
17.3.4.4 Implicit Solvent 498
17.3.4.5 Case Study: Coarse-Grained Model of Alpha-Helical Protein Domains 499
17.3.4.6 Case Study: Network Model of Alpha Helices 502
17.3 Theoretical Strength Models of Protein Constituents 505
17.4.1 Strength of a Single Bond 506
17.4.1.1 Bell's Model: A Force Dependent Dissociation Rate 506
17.4.1.2 Evans' Extension: A Loading Rate Dependence of Strength 507
17.4.1.3 Other Refinements of Bell's Model 509
17.4.2 Strength of Complex Molecular Bonds 509
17.4.2.1 Multiple Bonds in Parallel 510
17.4.2.2 Coupled Strength Models 511
17.4.2.3 Hierarchical Bell Model 512
17.4.3 Size Effects in H-Bond Clusters 514
17.4.4 Asymptotic Strength Model for Alpha Helix Protein Domains 515
17.4.4.1 Modeling and Results 517
17.4.4.2 Summary and Discussion 521
17.4 Complementary Experimental Methods 522
17.5.1 Structural Characterization 522
17.5.2 Manipulation and Mechanical Testing 522
17.5.3 Synthesis Methods for Hierarchical Materials 524
17.5 De Novo Design of Bioinspired and Biomimetic Nanomaterials 524
17.6.1 Development of Bioinspired Metallic Nanocomposites 527
17.6.2 Nanostructure Design Effects Under Tensile and Shock Loading 528
17.6.3 Outlook and Opportunities 530
17.6 Discussion and Conclusion 531
17.7 Acknowledgements 533
References 533
18 Computational Molecular Biomechanics: A Hierarchical Multiscale Framework with Applications to Gating of Mechanosensitive Channels of Large Conductance 543
18.1 Introduction 543
18.2 Brief Overview of Mechanosensitive (Ms) Channels 544
18.3.1 Structural Components of MS Channel of Large Conductance (MscL) 544
18.3.2 Previous Experimental and Theoretical Investigations 547
18.3.3 Previous Numerical Approaches 548
18.3 Continuum-Based Approach: Model and Methods for Studying Mscl 549
18.4 Gating Mechanisms of Mscl and Insights for Mechanotransduction 551
18.5.1 Effect of Different Loading Modes 551
18.5.1.1 Gating Behaviors Upon Equi-Biaxial Tension 551
18.5.1.2 Gating Behaviors Upon Bending 554
18.5.1.3 Insights of Loading Modes Vs. Mechanotransduction 555
18.5.2 Effects of Structural Motifs 556
18.5.3 Co-operativity of MS Channels 557
18.5.4 Large Scale Simulations of Lab Experiments 559
18.5 Future Look and Improvements of Continuum Framework 560
18.6 Conclusion 562
18.7 Acknowledgment 563
References 563
19 Out of Many, One: Modeling Schemes for Biopolymer and Biofibril Networks 565
19.1 Introduction 565
19.2 Biopolymers of Interest 566
19.3.1 Intracellular Networks 567
19.3.1.1 Actin 567
19.3.1.2 Microtubules 568
19.3.1.3 Intermediate Filaments 569
19.3.1.4 Spectrin 569
19.3.2 Extracellular Networks 569
19.3.2.1 Collagen I 569
19.3.2.2 Collagen IV 570
19.3.2.3 Laminin 570
19.3.2.4 Fibronectin 570
19.3.2.5 Fibrin 571
19.3.3 The Mechanical Behavior of Biopolymers 571
19.3 Network Imaging, Extraction, and Generation 574
19.4.1 Imaging 575
19.4.1.1 Fiber-Level Imaging 575
19.4.1.2 Indirect (Population-Level) Imaging 576
19.4.2 Network Extraction 576
19.4.3 Model Network Generation 577
19.4.4 Network Generation via Energy Minimization 578
19.4 General Modeling Approaches for Biopolymer Networks 580
19.5.1 Definitions 580
19.5.2 Affine Theory 581
19.5.3 Nonaffine Models 582
19.5.3.1 Spring Model 582
19.5.3.2 Beam Models 584
19.5.3.3 Entropic Beam Model 585
19.5.4 Finite Strain 586
19.5.4.1 Strain Stiffening 586
19.5.5 Bridging Scales -- Multiscale Behavior of Networks 586
19.5.5.1 Representative Volume Element 586
19.5.5.2 Volume Averaging 587
19.5 Applications to Biopolymers 590
19.6.1 Actin 590
19.6.2 Microtubules, IFs, and the Cytoskeleton 591
19.6.3 Spectrin 592
19.6.4 Collagen I 593
19.6.5 Type IV Collagen 596
19.6.6 Fibronectin, Laminin, and the ECM 596
19.6 Summary 596
19.7 Nomenclature 597
REFERENCES 599
Index 611